While not for Lemmix, there are definitely some highly memorable no-builder levels (and more generally, no-constructive-skills levels) made here that I still remember. For example geoo (or was it Simon)'s "little miner puzzle" levels in the Lix community set is great, and Clam made this Lemmings 2 custom level, "what a twist!", that is possibly the most awesome level to feature just one skill total (granted, we're talking one of those fan-driven skills in Lemmings 2, and there is also an automatic filler dispenser, so okay, maybe not quite "no-constructive-skills").
I guess the main thing with making big no-builder levels is that you are sort of forced to add in a whole bunch more terrain that the lemmings can meaningfully destroy, whereas with builders, you can just leave open some areas of emptiness that they can do their building at.
The essence of the "no-builder" challenge is that the builder in L1 is vastly more versatile than the other skills. It's your only means of crossing gaps of any kind, and also does various other things that are hard to do otherwise in L1, like turning around, stopping diggers, and crowd control without losing lemmings. Later games provide numerous other skills and devices that help your lemmings get around, so even though the builder has the same functionality in L2 and Lix, it's not the "crutch" it tends to be in L1. So while the no-builder challenge isn't unique to L1 (ccexplore's Lix examples show that), you do have to exclude a lot more skills/objects to get the same challengey feeling in other Lemmings games.
I wouldn't consider "What a twist!" as a no-builder challenge. It's really a completely different style of level to what you can have in L1. That's not to say it's not a good level of course

(though I'll leave judging exactly how good it is to others).
I did have only a few ideas up my sleeve for "no builder" challenges, however these are small levels as well. You do raise a good point Luis. It is quite rare to get a long level without builders (well, I do remember "Look before you leap", which was a fairly long level without builders).
As this is the Level Designing board, I will share my creations of "No Builder" levels too.

A few years ago I made a brick level called "The Structure" and an Xmas level called "Dugout".
The classic no-builder level that has to be mentioned is "To The End!" (
Lemmings Plus DOS Project - 15 - Psycho (Part 3) Level 8 ). A Cheapo remake -- which geoo's Little Miner Puzzle levels also are.
I haven't done very many builderless levels -- one that's bombers only; one that's just Fun 8, i.e. turning around without builders; a couple with platformers but no builders. (Among these, "Halfway Down the Stairs" is to an extent notable, considering that you have to go
up, and the single platformer doesn't help much with that. In my solution, I use the platformer merely to stop a basher mid-stroke.)
Möbius's two-player version of Compression Method 1 is (like the original) builderless, which makes for a very interesting experience quite unlike the normal run of 2P levels.
* * *
Very nice levels, minimac! Not too tough but not easy either.
Builder skill clearly seems to be the most essential skill in Lemmings games, there are very few levels which lack builders. Here is a list of builderless levels in some official games:
Original Lemmings
Fun 1-6 are builderless tutorial levels
Fun 13/Tricky 2/Taxing 30/Mayhem 11: We all fall down
Fun 18: Let's block and blow
Tricky 15: Ozone friendly Lemmings
Tricky 16: Luvly Jubly
Tricky 17: Diet Lemmingaid
Taxing 6: Compression Method 1
Taxing 19: Bomboozal
Mayhem 4: The Crossroads
Mayhem 16: Just a Minute...
Mayhem 24: All or Nothing
Mayhem 27: Just a Minute (Part Two)
Oh No! More Lemmings
Crazy 1: Quote: "That's a good level"
Wicked 1: LeMming ToMato KethcUp fAcilitY
Wicked 7: Last Lemming To Lemmingscentral
Havoc 20: LOok BeFoRe YoU LeAp!
Xmas/Holiday Lemmings
Xmas1992 1: Jingle Lemming
Hail 6: Surprise Package?
Blizzard 12: The Voyage Home...
Blizzard 14: The Undiscovered Country
Official Companion demo
Fun 1: Digger Conversions
Tricky 2: Lemming Excavation
Tricky 4: The Pipeline
Genesis/MegaDrive Lemmings
Fun 14: Room with no exit
Fun 21: Lemmings in the attic
Tricky 12: Go out for a walk?
Tricky 27: Everyone turn left
Tricky 30: Don't follow me.
Taxing 13: Walk through here but cautiously
Present 7: Everyone turn Left!
Present 8: Libra (Part two)
Present 10: Where are you heading?
Sunsoft 1: Rules to Fall
Sunsoft 6: Libra
Sunsoft 7: Everyone turn left (Part two)
Sunsoft 26: Just a minute (Part Three)
Sunsoft 27: Two heads are better...
Lemmings Revolution has also 13 builderless tutorial levels and then Kriss Kross, Bamboo Maze and Odd Jobs. There's still switchs, teleports etc. stuff which make builder skills less essential in this case.
It seems that the builderless levels are quite small in official games, the most lengthy is Havoc 20. Holiday level 'The Voyage Home...' and Official Companion level 'The Pipeline' are large maps, but there are lots of walking in those levels.
I know a lot of builderless custom levels made by some great level makers, I'll list the best of them too soon if it's ok, there are some lengthy levels also.
no builders often makes you come up with unusual ways of getting to places and turning lemmings around. e.g. Tsueg's 'Rush Hour'. I like builderless levels, personally. Just because builder is the most used skill.
Thanks a lot for that list Akseli!

I forgot Bamboo Maze had no builders. Anyway--this topic give me some more inspiration to make new levels.
I too tend to like builderless levels, and spotting these was actually rather exciting.

Here are some builderless custom levels listed like this:
"
CreatorLevelpack: title of a level"
Builderless levels of some great Lemmix level makers:
BulletRideBulletRide1: Ignition
BulletRide3: Just a Reverse Minute
BulletRide5(ver3): Cut to the Quick
Clam SpammerClamSpam01: Dig This!
ClamSpam02: Cut the Red Wire, Get Out of the Pool!, A.T. on an Angle, Stay Out of the Pool!!!
ClamSpam03: Barrel o' Laughs, Turning the Screws, The Dying Seconds
ClamSpam04: Flotilla, Dropout, From the Brink
ClamSpam05: The endless steps (a large builderless map)
ClamSpamXmas10: A.T. on a shoestring
- Also 8 builderless challenge levels in CSTame packs
Ellischant (Eymerich)E3Levelpack_F: Minimal Trouble
finlayfinpak01: Chrysanthemum paradise
Garjen (J. Gareth Moreton)GARJEN09: Faithful Friends
geoogeooPk0: crossing stairs
geooPk1: More 'No Builder Problems'
- Also 4 builderless glitch levels in geooPkG pack
-H0ru5-elfpak01: Fortress 13 (a large builderless map)
Insane SteveISteve03: A Towering Proposition
ISteve06: It's Hammer Time!
ISteve07: The Annoying 1-pixel Gap, Bash and no time (the first one is a LAAAAARGE builderless map)
ISteve08: I Traded Them for Climbers
ISteve09: A BeastIV of a level, Undermined, NO MAS!
Martin ZurlindenMazuLems: Fallout Boys
namidaLemmings DOS Plus Project: Just Walk!, Take Your Time..., Blow Down!, Fast enough?, Ready, Aim, Fire!!!, Safety Blast, Fallen, The Lonely Pole, Six Feet Under, Backdraft, Unholy Staircase, With A Quirk Or Two..., Antigravity, Phase Rotation Syndrome, The Deadly Climb, To The End! (the last one, which Proxima already mentioned, is an excellent example of a difficult, large builderless level)
siergiejSiergiej01: Tower of insomnia, The ephemeral labyrinth, The scaffold (the last one is a quite lengthy level)
Thick Molasses (möbius)TM pack 1: Afraid of Heights
TM3: A Towering Tower
tseug1tseug: Rush Hour (well, möbius already mentioned this)
YawgYawg06: Turn it Around!
Builderless levels of some Lemmini level virtuosos:
DodochacaloDoveLems: Plain rating levels 1-5 and 7 are builderless tutorial levels, Disappearance ?, Bashers are Back !, It's Not an Illusion !, Lemmings-Digging Iron Plates, Molotov Cocktail and Co, Art of Mining, It's an Evil Symphony !, One-Way Traffic, La France, Imposing Block
FranLems: Doux rating levels 1-3 are builderless tutorial levels, Art Moderne
GronklingGronklems5: Drifting Away..., Optical Fibre Land
LacktardoThere's no eye in team (doesn't belong in any levelpack as far as I know)
PieuwPieuw01: Bricky Madness, Descent into Hell
Pieuw02: The Magic Box
30levelspack(Pieuw): Hugs & Kisses, The Drowning Walk
- Other builderless levels by Pieuw that don't belong in levelpacks: Triumph For Their Magic Picks, Off-Centered but yet in Focus, Straight Forward
Nice research there Akseli

---
So there are good no-builder levels of course, but you also have no-builder challenges on levels that give you builders. These can be more exciting in some cases, because you don't know in advance whether it's even possible. Fun 29 springs to mind, but there are plenty more in the "skills you can't live without" challenge. (Sorry, Tame 13 needs one builder so doesn't count

)
I'm honoured you think i'm a "great" level maker

that's not a particularly "great" level though, it was something i threw together with only bombers – it's all obnoxious bomber timing/hidden trap ideas.
the level I posted here:
http://www.lemmingsforums.com/index.php?topic=563.msg11839#msg11839 is a better example of a builderless level that I've made, I think. I can't remember if I released it as a pack or if it was only as a single level file though. It has some placeholder name like "it's a long way to the top".
anyway i should check back in here more often, i think.
Not quite builderless, but attempting to solve Danger 29 (Pipeline Problem) with only one builder is a LOT harder than any of the builderless levels; To The End included.
Also worth noting that the most recent version of LPDOS removes at least one of the levels mentioned in your list (Phase Rotation Syndrome), possibly more. (EDIT: Also removed is "The Lonely Pole". In both cases, the new levels replacing them are not builderless.)
Welcome back, namida, we haven't seen you around in a while
finlay: I didn't remember the hidden traps in Chrysanthemum paradise and I realized why: I played finpak01 in CustLemm months ago and no one of the hidden traps worked. Now I tried the level in Lemmix - and it was more annoying, I admit.

But I liked your other levels, especially "Fiery Depths", and the idea when making the list was that I wanted to gather many different types of level makers and levels in it.
namida: Yep, builderless levels The Lonely Pole (Medi 16) and Phase Rotation Syndrome (Danger 21) aren't included in the latest version (v.7) of LPDOS, they exist only in the earlier versions.
Here's an idea for a builderless level in the Crystal theme.
I got a bit excited there, but ended up feeling disappointed.

For some reason that idea is terribly shallow and the only exciting bit is that the solution demonstrates a glitch (which can be seen
here). I'm sure this level can be improved in some way.
Are you sure the Climber falling and landing on a terrain like in my level is a glitch?

Because that narrow gap trick works in the PSP too. That's how I was able to build the "Room with no exit" and "Let's go to the moon" levels with the diangle terrains. I put the slopes really close to each other to the point where even though there's a little hole, the Lemmings will walk up the slopes instead of walking down back to the place it came from. Seems like a normal thing to me. The small level that I made was only to show a new way for a climber to travel around. I was gonna make a level that uses that, but I'm still trying to picture how the level will look like.
Are you sure the Climber falling and landing on a terrain like in my level is a glitch?
Because that narrow gap trick works in the PSP too. That's how I was able to build the "Room with no exit" and "Let's go to the moon" levels with the diangle terrains. I put the slopes really close to each other to the point where even though there's a little hole, the Lemmings will walk up the slopes instead of walking down back to the place it came from. Seems like a normal thing to me. The small level that I made was only to show a new way for a climber to travel around. I was gonna make a level that uses that, but I'm still trying to picture how the level will look like.
whether it's a glitch or not is debatable. I should say; whether it's a good or bad thing is debatable. I thought of making a level like that but then I decided a situation where you have to build to the wall as the lemming climbs up then the builder closes it as he comes down is more challenging.
The idea I had (previously) was; you have to build up close to the wall like that, without connecting. This idea is less demanding on timing. It also relays on a technical maneuver, however, which can be very hard to grasp. But I thought of this a while ago as did other people apparently so maybe it's not a bad idea. [of course my idea wouldn't be 'no builders'...]
It can get tricky in Lemmix especially. I'm not sure if this is a problem you'd encounter with this or not (obviously it wasn't in the level you posted).
Because of the way climbers check for terrain above them, they can either climb through small overhangs at the top of a wall, or fall down when there is a tiny gap (which it should be able to get into) with terrain hanging above. The outcome depends on the height of the wall.
-from Glitches in Lemmings
I put the slopes really close to each other to the point where even though there's a little hole, the Lemmings will walk up the slopes instead of walking down back to the place it came from. Seems like a normal thing to me.
It's hard to tell what you mean since I don't have PSP, but in any case I really wouldn't call it the same thing since it's about walking not climbing. The behavior you see here with the climber in DOS Lemmings only happens because for some reason, the game shifts the climber an additional pixel away from the wall when it bumps its head and falls. In other words, instead of landing at exactly where he was before he starts climbing, he lands even farther away from the wall than he was located the last time he's still walking.
Another way to see the strangeness of it is, if the terrain was more like this
XXXX
...X
...X
...X
...X
...X
...X
...X
...X
...X
X.YX
Starting from Y and after climbing up the wall on the right, he would fall straight through the X.Y gap rather than landing on Y, even though in both this case and in your level, you have exactly one pixel of terrain and one pixel of gap.
It's hard to find a logical way to explain for that additional distance shifting away from the wall. In DOS Lemmings walkers will always fall off even a one-pixel gap. In PSP with higher graphics resolution, it may be possible to create terrain that have tiny gaps narrower than the distance a lemming moves walking a single step, but I would think that when the gap is wider than the single-step walk distance a walking lemming would probably fall too?
In any case, I have to say glitch or not, even the original levels from the game seem to have more interesting examples of builderless level ideas than the one you present. You may want to create a few more other examples featuring other ideas and then maybe put them together in one level.
It's hard to tell what you mean since I don't have PSP, but in any case I really wouldn't call it the same thing since it's about walking not climbing.
This is what I mean:
http://i232.photobucket.com/albums/ee91/Luis2_06/MYDC0721.jpgThere's a little hole that the Lemmings can walk through and there's a very small pixel at the edge of the diangle terrain where the Lemmings can walk up from, by the time they turn around. To be honest, I didn't know that little pixel at the edge of the terrain was there, until I took a picture of it. No wonder the PSP Lemmings can walk up the diangle terrains. If you close the hole, the Lemmings won't be able to get through. They will just turn around from it.
As for the climber level I posted, I'm still gonna build a level for myself that uses that, whether it gives a lot of depth or not. I wanna play a level where that's part of the solution.
here's a builder-less level that doesn't use any special tricks or anything.
EDIT: ignore, see my post below with a correct version.
This didn't turn out like I wanted but it's builder-less at least. I've been trying to make levels involving timing. (I don't mean fast-paced or quick movement/bomber timing) I mean a level that requires you to do out-of-place things in a very specific order. I think these might be the hardest kind and are incredibly difficult to create. For me they are anyway. I don't know what I'm talking about.

the level I posted here: http://www.lemmingsforums.com/index.php?topic=563.msg11839#msg11839 is a better example of a builderless level that I've made, I think. I can't remember if I released it as a pack or if it was only as a single level file though. It has some placeholder name like "it's a long way to the top".
I still haven't solved this level! It's a really good one.
You probably didn't intend for this to happen, considering it leaves a few skills.
My latest lix level happens to be without builders as well, and is obviously timing based.
Oops, right, I forgot about that. I initially even included a blocker but remembered miner-turning before I was done. Here's a fix.
EDIT: another fix
the intended solution may leave skills
Still not particularly exciting solution:
...
Garjen (J. Gareth Moreton)
GARJEN09: Faithful Friends
Heh, that brings back memories. I did make another non-Builder level named "3W" (GARJEN04, I think), but that was a fairly basic Blocker and Bomber affair. I did realise quickly that non-Builder levels are tricky to make, and that was probably my only real attempt. Despite the backroute, I feel it wasn't too bad an attempt - here it is in action:
www.youtube.com/watch?v=SkXYB32_oAk (Hmmm, I have a thing for levels with time limits of 2 minutes!)
If I get the chance I might have another go at making a builder-less level.
Your other builderless levels are:
GARJEN00: Look familiar? LOOK AGAIN!, Lemming Cathodes, Breakout!, Death Trap
GARJEN03: The Incinerator
GARJEN07: Everyone turn left (Part Two)
GARJEN08: Everyone turn left
At least last two levels were same as in the original game I guess, and for me, Faithful Friends is clearly your best builderless level. My solution saves 3 climbers in it.